[FORM OF ADDITIONAL WARRANTS]

Exhibit 4.04

[FORM OF ADDITIONAL WARRANTS]

NEITHER THE ISSUANCE AND SALE OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE NOR THE SECURITIES INTO WHICH THESE SECURITIES ARE EXERCISABLE HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS. THE SECURITIES MAY NOT BE OFFERED FOR SALE, SOLD, TRANSFERRED OR ASSIGNED (I) IN THE ABSENCE OF (A) AN EFFECTIVE REGISTRATION STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND APPLICABLE STATE SECURITIES LAWS, OR (B) AN OPINION OF COUNSEL REASONABLY ACCEPTABLE TO THE COMPANY, IN A FORM REASONABLY ACCEPTABLE TO THE COMPANY, THAT REGISTRATION IS NOT REQUIRED UNDER SAID ACT OR (II) UNLESS SOLD PURSUANT TO RULE 144 OR RULE 144A UNDER SAID ACT. NOTWITHSTANDING THE FOREGOING, THE SECURITIES MAY BE PLEDGED IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT OR OTHER LOAN OR FINANCING ARRANGEMENT SECURED BY THE SECURITIES.

CORVIS CORPORATION

WARRANT TO PURCHASE COMMON STOCK

Warrant No.:

Number of Shares:             ¹

Date of Issuance:                  , 200_ (the “Issuance Date”)

Corvis Corporation, a Delaware corporation (the “Company”), hereby certifies that, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged,                     , the registered holder hereof or its permitted assigns (the “Holder”), is entitled, subject to the terms set forth below, to purchase from the Company, at the Exercise Price (as defined below) then in effect, upon surrender of this Warrant to Purchase Common Stock (including all Warrants to Purchase Common Stock issued in exchange, transfer or replacement hereof, the “Warrant”), at any time or times on or after the date hereof, but not after 11:59 P.M., New York Time, on the Expiration Date (as defined below),                      (                    )² fully paid nonassessable shares of Common Stock (as defined below) (the “Warrant Shares”). Except as otherwise defined herein, capitalized terms in this Warrant shall have the meanings set forth in Section 15. This Warrant is one of the Warrants to Purchase Common Stock (the “SPA Warrants”) issued pursuant to Section 1 of that certain Securities Purchase Agreement, dated as of February 9, 2004 (the “Subscription Date”), among the Company and the buyers (the “Buyers”) referred to therein (the “Securities Purchase Agreement”).

1. EXERCISE OF WARRANT.

(a) Mechanics of Exercise. Subject to the terms and conditions hereof (including, without limitation, the limitations set forth in Section 1(f)), this Warrant may be exercised by the Holder on any day, in whole or in part, by (i) delivery of a written notice, in the form attached hereto as Exhibit A (the “Exercise Notice”), of the Holder’s election to exercise this Warrant and (ii) (A) payment to the Company of an amount equal to the applicable Exercise Price multiplied by the number of Warrant Shares as to which this Warrant is being exercised (the “Aggregate Exercise Price”) in cash or wire transfer of immediately available funds or (B) by notifying the Company that this Warrant is being exercised pursuant to a Cashless Exercise (as defined in Section 1(d)). The Holder shall not be required to deliver the original Warrant in order to effect an exercise hereunder. Execution and delivery of the Exercise Notice with respect to less than all of the Warrant Shares shall have the same effect as cancellation of the original Warrant and issuance of a new Warrant evidencing the right to purchase the remaining number of Warrant Shares. On or before the first Business Day following the date on which the Company has received each of the Exercise Notice and the Aggregate Exercise Price (or notice of a Cashless Exercise) (the “Exercise Delivery Documents”), the Company shall transmit by facsimile an acknowledgment of confirmation of receipt of the Exercise Delivery Documents to the Holder and the Company’s transfer agent (the “Transfer Agent”). On or before the third Business Day following the date on which the Company has received all of the Exercise Delivery Documents (the “Share Delivery Date”), the Company shall (X) provided that the Transfer Agent is participating in The Depository Trust Company (“DTC”) Fast Automated Securities Transfer Program, upon the request of the Holder, credit such aggregate number of shares of Common Stock to which the Holder is entitled pursuant to such exercise to the Holder’s or its designee’s balance account with DTC through its Deposit Withdrawal Agent Commission system, or (Y) if the Transfer Agent is not participating in the DTC Fast Automated Securities Transfer Program, issue and dispatch by overnight courier to the address as specified in the Exercise Notice, a certificate, registered in the name of the Holder or its designee, for the number of shares of Common Stock to which the Holder is entitled pursuant to such exercise. Upon delivery of the Exercise Notice and Aggregate Exercise Price referred to in clause (ii)(A) above or notification to the Company of a Cashless Exercise referred to in Section 1(d), the Holder shall be deemed for all corporate purposes to have become the holder of record of the Warrant Shares with respect to which this Warrant has been exercised, irrespective of the date of delivery of the certificates evidencing such Warrant Shares. If this Warrant is submitted in connection with any exercise pursuant to this Section 1(a) and the number of Warrant Shares represented by this Warrant submitted for exercise is greater than the number of Warrant Shares being acquired upon an exercise, then the Company shall as soon as practicable and in no event later than three Business Days after any exercise and at its own expense, issue a new Warrant (in accordance with Section 7(d)) representing the right to purchase the number of Warrant Shares purchasable immediately prior to such exercise under this Warrant, less the number of Warrant Shares with respect to which this Warrant is exercised. No fractional shares of Common Stock are to be issued upon the exercise of this Warrant, but rather the number of shares of Common Stock to be

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issued shall be rounded up to the nearest whole number. The Company shall pay any and all taxes, including without limitation, all documentary stamp, transfer or similar taxes, or other incidental expense that may be payable with respect to the issuance and delivery of Warrant Shares upon exercise of this Warrant.

(b) Exercise Price. For purposes of this Warrant, “Exercise Price” means $            ³, subject to adjustment as provided herein.

(c) Company’s Failure to Timely Deliver Securities. Subject to Section 1(f), if the Company shall fail for any reason or for no reason to issue to the Holder within three (3) Business Days of receipt of the Exercise Delivery Documents, a certificate for the number of shares of Common Stock to which the Holder is entitled or to credit the Holder’s balance account with DTC for such number of shares of Common Stock to which the Holder is entitled upon the Holder’s exercise of this Warrant, then, in addition to all other remedies available to the Holder, the Company shall pay in cash to the Holder on each day after such third Business Day that the issuance of such shares of Common Stock is not timely effected an amount equal to 0.5% of the product of (A) the sum of the number of shares of Common Stock not issued to the Holder on a timely basis and to which the Holder is entitled and (B) the Closing Sale Price of the shares of Common Stock on the trading day immediately preceding the last possible date which the Company could have issued such shares of Common Stock to the Holder without violating Section 1(a).

(d) Cashless Exercise. Notwithstanding anything contained herein to the contrary, if at any time during the period commencing ten (10) Business Days prior to the Holder’s delivery of an Exercise Notice and ending on the day of delivery of the Exercise Notice, a Registration Statement (as defined in the Registration Rights Agreement) covering the Warrant Shares that are the subject of the Exercise Notice (the “Unavailable Warrant Shares”) is not available for the resale of such Unavailable Warrant Shares, the Holder may, in its sole discretion, exercise this Warrant in whole or in part and, in lieu of making the cash payment otherwise contemplated to be made to the Company upon such exercise in payment of the Aggregate Exercise Price, elect instead to receive upon such exercise the “Net Number” of shares of Common Stock determined according to the following formula (a “Cashless Exercise”):

Net Number = (A x B) - (A x C)

B

For purposes of the foregoing formula:

A= the total number of shares with respect to which

this Warrant is then being exercised.

B= the Closing Sale Price of the Common Stock (as

reported by Bloomberg) on the date immediately

preceding the date of the Exercise Notice.

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C= the Exercise Price then in effect for the

applicable Warrant Shares at the time of such

exercise.

(e) Disputes. In the case of a dispute as to the determination of the Exercise Price or the arithmetic calculation of the Warrant Shares, the Company shall promptly issue to the Holder the number of Warrant Shares that are not disputed and resolve such dispute in accordance with Section 12.

(f) Limitations on Exercises.

(i) Beneficial Ownership. The Company shall not effect the exercise of this Warrant, and no Holder shall have the right to exercise this Warrant, to the extent that after giving effect to such exercise, such Person (together with such Person’s affiliates) would beneficially own in excess of 4.99% (the “Maximum Percentage”) of the shares of the Common Stock outstanding immediately after giving effect to such exercise. For purposes of the foregoing sentence, the aggregate number of shares of Common Stock beneficially owned by such Person and its affiliates shall include the number of shares of Common Stock issuable upon exercise of this Warrant with respect to which the determination of such sentence is being made, but shall exclude shares of Common Stock which would be issuable upon (i) exercise of the remaining, unexercised portion of this Warrant beneficially owned by such Person and its affiliates and (ii) exercise or conversion of the unexercised or unconverted portion of any other securities of the Company beneficially owned by such Person and its affiliates (including, without limitation, any debentures, convertible notes or convertible preferred stock or warrants) subject to a limitation on conversion or exercise analogous to the limitation contained herein. Except as set forth in the preceding sentence, for purposes of this paragraph, beneficial ownership shall be calculated in accordance with Section 13(d) of the Securities Exchange Act of 1934, as amended. For purposes of this Warrant, in determining the number of outstanding shares of Common Stock, the Holder may rely on the number of outstanding shares of Common Stock as reflected in (1) the Company’s most recent Form 10-Q, Form 10-K or other public filing with the Securities and Exchange Commission, as the case may be, (2) a more recent public announcement by the Company or (3) any other notice by the Company or its Transfer Agent setting forth the number of shares of Common Stock outstanding. For any reason at any time, upon the written or oral request of the Holder, the Company shall within one Business Day confirm orally and in writing to the Holder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or exercise of securities of the Company, including the SPA Securities and the SPA Warrants, by the Holder and its affiliates since the date as of which such number of outstanding shares of Common Stock was reported. By written notice to the Company, the Holder may increase or decrease the Maximum Percentage to any other percentage not in excess of 9.99% specified in such notice; provided that any such increase will not be effective until the 61st day after such notice is delivered to the Company, and (ii) any such increase or decrease will apply only to the Holder and not to any other holder of Warrants.

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(ii) Principal Market Regulation. The Company shall not be obligated to issue any shares of Common Stock upon exercise of this Warrant if the issuance of such shares of Common Stock would exceed that number of shares of Common Stock which the Company may issue upon exercise of this Warrant and the SPA Securities (including, as applicable, any shares of Common Stock issued upon conversion of or as payment of any interest under the SPA Securities) without breaching the Company’s obligations under the rules or regulations of the Principal Market (the “Principal Market Cap”), except that such limitation shall not apply in the event that the Company (A) obtains the approval of its stockholders as required by the applicable rules of the Principal Market for issuances of Common Stock in excess of such amount or (B) obtains a written opinion from outside counsel to the Company that such approval is not required, which opinion shall be reasonably satisfactory to the holders of the SPA Warrants representing at least a majority of the shares of Common Stock underlying the SPA Warrants then outstanding. Until such approval or written opinion is obtained, no Holder shall be issued, upon exercise of any SPA Warrants or conversion of any SPA Securities, shares of Common Stock in an amount greater than the product of the Principal Market multiplied by a fraction, the numerator of which is the total number of shares of Common Stock underlying the SPA Warrants issued to such Purchaser pursuant to the Securities Purchase Agreement on the Initial Closing Date (as defined in the Securities Purchase Agreement) and the denominator of which is the aggregate number of shares of Common Stock underlying all the SPA Warrants issued to the Buyers pursuant to the Securities Purchase Agreement on the Initial Closing Date (with respect to each Purchaser, the “Principal Market Cap Allocation”). In the event that any Purchaser shall sell or otherwise transfer any of such Purchaser’s SPA Warrants, the transferee shall be allocated a pro rata portion of such Purchaser’s Principal Market Cap Allocation, and the restrictions of the prior sentence shall apply to such transferee with respect to the portion of the Principal Market Cap Allocation allocated to such transferee. In the event that any holder of SPA Warrants shall exercise all of such holder’s SPA Warrants into a number of shares of Common Stock which, in the aggregate, is less than such holder’s Principal Market Cap Allocation, then the difference between such holder’s Principal Market Cap Allocation and the number of shares of Common Stock actually issued to such holder shall be allocated to the respective Principal Market Cap Allocations of the remaining holders of SPA Warrants on a pro rata basis in proportion to the shares of Common Stock underlying the SPA Warrants then held by each such holder. In the event that the Company is prohibited from issuing any Warrant Shares for which an Exercise Notice has been received as a result of the operation of this Section 1(f)(ii), the Company shall pay cash in exchange for cancellation of such Warrant Shares, at a price per Warrant Share equal to the difference between the Closing Sale Price and the Exercise Price as of the date of the attempted exercise.

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2. ADJUSTMENT OF EXERCISE PRICE AND NUMBER OF WARRANT SHARES. The Exercise Price and the number of Warrant Shares shall be adjusted from time to time as follows:

(a) Adjustment upon Issuance of Common Stock. If and whenever on or after the Subscription Date the Company issues or sells, or in accordance with this Section 2 is deemed to have issued or sold, any shares of Common Stock (including the issuance or sale of shares of Common Stock owned or held by or for the account of the Company, but excluding Excluded Securities (as defined in the SPA Securities)) for a consideration per share less than a price (the “Applicable Price”) equal to the Exercise Price in effect immediately prior to such issue or sale or deemed issuance or sale (the foregoing, a “Dilutive Issuance”), then immediately after such Dilutive Issuance the Exercise Price then in effect shall be reduced to an amount equal to the product of (x) the Exercise Price in effect immediately prior to such Dilutive Issuance and (y) the quotient determined by dividing (1) the sum of the product of the Applicable Price and the number of shares of Common Stock Deemed Outstanding immediately prior to such Dilutive Issuance and the consideration, if any, received by the Company upon such Dilutive Issuance, by (2) the product of the Applicable Price multiplied by the number of shares of Common Stock Deemed Outstanding immediately after such Dilutive Issuance. Upon each such adjustment of the Exercise Price hereunder, the number of Warrant Shares shall be adjusted to the number of shares of Common Stock determined by multiplying the Exercise Price in effect immediately prior to such adjustment by the number of Warrant Shares acquirable upon exercise of this Warrant immediately prior to such adjustment and dividing the product thereof by the Exercise Price resulting from such adjustment. For purposes of determining the adjusted Exercise Price under this Section 2(a), the following shall be applicable:

(i) Issuance of Options. If the Company in any manner grants any Options and the lowest price per share for which one share of Common Stock is issuable upon the exercise of any such Option or upon conversion, exercise or exchange of any Convertible Securities issuable upon exercise of any such Option is less than the Applicable Price, then such share of Common Stock shall be deemed to be outstanding and to have been issued and sold by the Company at the time of the granting or sale of such Option for such price per share. For purposes of this Section 2(a)(i), the “lowest price per share for which one share of Common Stock is issuable upon exercise of such Options or upon conversion, exercise or exchange of such Convertible Securities” shall be equal to the sum of the lowest amounts of consideration (if any) received or receivable by the Company with respect to any one share of Common Stock upon the granting or sale of the Option, upon exercise of the Option and upon conversion, exercise or exchange of any Convertible Security issuable upon exercise of such Option. No further adjustment of the Exercise Price or number of Warrant Shares shall be made upon the actual issuance of such Common Stock or of such Convertible Securities upon the exercise of such Options or upon the actual issuance of such Common Stock upon conversion, exercise or exchange of such Convertible Securities.

(ii) Issuance of Convertible Securities. If the Company in any manner issues or sells any Convertible Securities and the lowest price per share for which one share of Common Stock is issuable upon the conversion, exercise or exchange thereof is less than the Applicable Price, then such share of Common Stock shall be deemed to be outstanding and to have been issued and sold by the Company at the time of the issuance or sale of such Convertible Securities for such price per share. For the purposes of this Section 2(a)(ii), the “lowest price per share for which one share of Common Stock is

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issuable upon the conversion, exercise or exchange” shall be equal to the sum of the lowest amounts of consideration (if any) received or receivable by the Company with respect to one share of Common Stock upon the issuance or sale of the Convertible Security and upon conversion, exercise or exchange of such Convertible Security. No further adjustment of the Exercise Price or number of Warrant Shares shall be made upon the actual issuance of such Common Stock upon conversion, exercise or exchange of such Convertible Securities, and if any such issue or sale of such Convertible Securities is made upon exercise of any Options for which adjustment of this Warrant has been or is to be made pursuant to other provisions of this Section 2(a), no further adjustment of the Exercise Price or number of Warrant Shares shall be made by reason of such issue or sale.

(iii) Change in Option Price or Rate of Conversion. If the purchase price provided for in any Options, the additional consideration, if any, payable upon the issue, conversion, exercise or exchange of any Convertible Securities, or the rate at which any Convertible Securities are convertible into or exercisable or exchangeable for Common Stock increases or decreases at any time, the Exercise Price and the number of Warrant Shares in effect at the time of such increase or decrease shall be adjusted to the Exercise Price and the number of Warrant Shares which would have been in effect at such time had such Options or Convertible Securities provided for such increased or decreased purchase price, additional consideration or increased or decreased conversion rate, as the case may be, at the time initially granted, issued or sold. For purposes of this Section 2(a)(iii), if the terms of any Option or Convertible Security that was outstanding as of the date of issuance of this Warrant are increased or decreased in the manner described in the immediately preceding sentence, then such Option or Convertible Security and the Common Stock deemed issuable upon exercise, conversion or exchange thereof shall be deemed to have been issued as of the date of such increase or decrease. No adjustment pursuant to this Section 2(a) shall be made if such adjustment would result in an increase of the Exercise Price then in effect or a decrease in the number of Warrant Shares.

(iv) Calculation of Consideration Received. If case any Option is issued in connection with the issue or sale of other securities of the Company, together comprising one integrated transaction in which no specific consideration is allocated to such Options by the parties thereto, the Options will be deemed to have been issued for a consideration of $0.01. If any Common Stock, Options or Convertible Securities are issued or sold or deemed to have been issued or sold for cash, the consideration received therefor will be deemed to be the net amount received by the Company therefor. If any Common Stock, Options or Convertible Securities are issued or sold for a consideration other than cash, the amount of such consideration received by the Company will be the fair value of such consideration, except where such consideration consists of securities, in which case the amount of consideration received by the Company will be the Closing Sale Price of such security on the date of receipt. If any Common Stock, Options or Convertible Securities are issued to the owners of the non-surviving entity in connection with any merger in which the Company is the surviving entity, the amount of consideration therefor will be deemed to be the fair value of such portion of the net assets and business of the non-surviving entity as is attributable to such Common Stock, Options or Convertible

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Securities, as the case may be. The fair value of any consideration other than cash or securities will be determined jointly by the Company and the holders of SPA Warrants representing at least a majority of the shares of Common Stock obtainable upon exercise of the SPA Warrants then outstanding. If such parties are unable to reach agreement within 10 days after the occurrence of an event requiring valuation (the “Valuation Event”), the fair value of such consideration will be determined within fifteen Business Days after the tenth day following the Valuation Event by an independent, reputable appraiser jointly selected by the Company and the holders of SPA Warrants representing at least a majority of the shares of Common Stock obtainable upon exercise of the SPA Warrants then outstanding. The determination of such appraiser shall be final and binding upon all parties absent manifest error and the fees and expenses of such appraiser shall be borne by the Company.

(v) Record Date. If the Company takes a record of the holders of Common Stock for the purpose of entitling them (A) to receive a dividend or other distribution payable in Common Stock, Options or in Convertible Securities or (B) to subscribe for or purchase Common Stock, Options or Convertible Securities, then such record date will be deemed to be the date of the issue or sale of the shares of Common Stock deemed to have been issued or sold upon the declaration of such dividend or the making of such other distribution or the date of the granting of such right of subscription or purchase, as the case may be.

(vi) This Warrant Deemed Outstanding. If during the period beginning on and including the Subscription Date and ending on the date immediately preceding the date of issuance of this Warrant, the Company entered into, or in accordance with Section 2(a) would have been deemed to have entered into (had this Warrant been outstanding at such time), any Dilutive Issuance, then solely for purposes of determining any adjustment under this Section 2(a) as a result of such Dilutive Issuance or deemed Dilutive Issuance, this Warrant shall be deemed to have been outstanding at the time of each such Dilutive Issuance or deemed Dilutive Issuance.

(b) Adjustment upon Subdivision or Combination of Common Stock. If the Company at any time after the Subscription Date subdivides (by any stock split, stock dividend, recapitalization or otherwise) one or more classes of its outstanding shares of Common Stock into a greater number of shares, the Exercise Price in effect immediately prior to such subdivision will be proportionately reduced and the number of Warrant Shares will be proportionately increased. If the Company at any time on or after the Subscription Date combines (by combination, reverse stock split or otherwise) one or more classes of its outstanding shares of Common Stock into a smaller number of shares, the Exercise Price in effect immediately prior to such combination will be proportionately increased and the number of Warrant Shares will be proportionately decreased. Any adjustment under this Section 2(b) shall become effective at the close of business on the date the subdivision or combination becomes effective.

(c) Other Events. If any event occurs of the type contemplated by the provisions of this Section 2 but not expressly provided for by such provisions (including, without

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limitation, the granting of stock appreciation rights, phantom stock rights or other rights with equity features), then the Company’s Board of Directors will make an appropriate adjustment in the Exercise Price and the number of Warrant Shares so as to protect the rights of the Holder; provided that no such adjustment pursuant to this Section 2(c) will increase the Exercise Price or decrease the number of Warrant Shares as otherwise determined pursuant to this Section 2.

3. RIGHTS UPON DISTRIBUTION OF ASSETS. If the Company shall declare or make any dividend or other distribution of its assets (or rights to acquire its assets) to holders of Common Stock, by way of return of capital or otherwise (including, without limitation, any distribution of cash, stock or other securities, property or options by way of a dividend, spin off, reclassification, corporate rearrangement or other similar transaction) (a “Distribution”), at any time after the issuance of this Warrant, then, in each such case:

(a) any Exercise Price in effect immediately prior to the close of business on the record date fixed for the determination of holders of Common Stock entitled to receive the Distribution shall be reduced, effective as of the close of business on such record date, to a price determined by multiplying such Exercise Price by a fraction of which (i) the numerator shall be the Closing Bid Price of the Common Stock on the trading day immediately preceding such record date minus the value of the Distribution (as determined in good faith by the Company’s Board of Directors) applicable to one share of Common Stock, and (ii) the denominator shall be the Closing Bid Price of the Common Stock on the trading day immediately preceding such record date; and

(b) the number of Warrant Shares shall be increased to a number of shares equal to the number of shares of Common Stock obtainable immediately prior to the close of business on the record date fixed for the determination of holders of Common Stock entitled to receive the Distribution multiplied by the reciprocal of the fraction set forth in the immediately preceding paragraph (a); provided that in the event that the Distribution is of common stock (“Other Common Stock”) of a company whose common stock is traded on a national securities exchange or a national automated quotation system, then the Holder may elect to receive a warrant to purchase Other Common Stock in lieu of an increase in the number of Warrant Shares, the terms of which shall be identical to those of this Warrant, except that such warrant shall be exercisable into the number of shares of Other Common Stock that would have been payable to the Holder pursuant to the Distribution had the Holder exercised this Warrant immediately prior to such record date and with an aggregate exercise price equal to the product of the amount by which the exercise price of this Warrant was decreased with respect to the Distribution pursuant to the terms of the immediately preceding paragraph (a) and the number of Warrant Shares calculated in accordance with the first part of this paragraph (b).

4. PURCHASE RIGHTS; ORGANIC CHANGE.

(a) Purchase Rights. In addition to any adjustments pursuant to Section 2 above, if at any time the Company grants, issues or sells any Options, Convertible Securities or rights to purchase stock, warrants, securities or other property pro rata to the record holders of any class of Common Stock (the “Purchase Rights”), then the Holder will be entitled to acquire, upon the terms applicable to such Purchase Rights, the aggregate Purchase Rights which the Holder could have acquired if such holder had held the number of shares of Common Stock

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acquirable upon complete exercise of this Warrant (without regard to any limitations on the exercise of this Warrant) immediately before the date on which a record is taken for the grant, issuance or sale of such Purchase Rights, or, if no such record is taken, the date as of which the record holders of Common Stock are to be determined for the grant, issue or sale of such Purchase Rights.

(b) Organic Change. Any recapitalization, reorganization, reclassification, consolidation, merger, sale of all or substantially all of the Company’s assets to another Person or other transaction, in each case which is effected in such a way that holders of Common Stock are entitled to receive securities or assets with respect to or in exchange for Common Stock is referred to herein as an “Organic Change.” Prior to the consummation of any (i) sale of all or substantially all of the Company’s assets to an acquiring Person or (ii) other Organic Change following which the Company is not a surviving entity, the Company will secure from the Person purchasing such assets or the Person issuing the securities or providing the assets in such Organic Change (in each case, the “Acquiring Entity”) a written agreement (in form and substance reasonably satisfactory to the holders of SPA Warrants representing at least a majority of the shares of Common Stock obtainable upon exercise of the SPA Warrants then outstanding) to deliver to the Holder in exchange for this Warrant, a security of the Acquiring Entity evidenced by a written instrument substantially similar in form and substance to this Warrant and reasonably satisfactory to the holder of this Warrant (including an adjusted exercise price equal to the value for the Common Stock reflected by the terms of such consolidation, merger or sale, and exercisable for a corresponding number of shares of Common Stock acquirable and receivable upon exercise of this Warrant (without regard to any limitations on the exercise of this Warrant), if the value so reflected is less than the Exercise Price in effect immediately prior to such consolidation, merger or sale). In the event that an Acquiring Entity is directly or indirectly controlled by a company or entity whose common stock or similar equity interest is listed, designated or quoted on a securities exchange or trading market, the Holder may elect to treat such Person as the Acquiring Entity for purposes of this Section 4(b). Prior to the consummation of any other Organic Change, the Company shall make appropriate provision (in form and substance reasonably satisfactory to the holders of SPA Warrants representing at least a majority of the shares of Common Stock obtainable upon exercise of the SPA Warrants then outstanding) to insure that the Holder thereafter will have the right to acquire and receive in lieu of or in addition to (as the case may be) the shares of Common Stock immediately theretofore acquirable and receivable upon the exercise of this Warrant (without regard to any limitations on the exercise of this Warrant), such shares of stock, securities or assets that would have been issued or payable in such Organic Change with respect to or in exchange for the number of shares of Common Stock which would have been acquirable and receivable upon the exercise of this Warrant as of the date of such Organic Change (without regard to any limitations on the exercise of this Warrant).

5. NONCIRCUMVENTION. The Company hereby covenants and agrees that the Company will not, by amendment of its Certificate of Incorporation or through any reorganization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities, or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of this Warrant, and will at all times in good faith carry out all the provisions of this Warrant and take all action as may be required to protect the rights of the Holder. Without

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limiting the generality of the foregoing, the Company (i) will not increase the par value of any shares of Common Stock receivable upon the exercise of this Warrant above the Exercise Price then in effect, (ii) will take all such actions as may be necessary or appropriate in order that the Company may validly and legally issue fully paid and nonassessable shares of Common Stock upon the exercise of this Warrant, and (iii) will, so long as any of the SPA Warrants are outstanding, take all action necessary to reserve and keep available out of its authorized and unissued Common Stock, solely for the purpose of effecting the exercise of the SPA Warrants, 125% of the number of shares of Common Stock as shall from time to time be necessary to effect the exercise of the SPA Warrants then outstanding (without regard to any limitations on exercise).

6. WARRANT HOLDER NOT DEEMED A STOCKHOLDER. Except as otherwise specifically provided herein, the Holder, solely in such Person’s capacity as a holder of this Warrant, shall not be entitled to vote or receive dividends or be deemed the holder of shares of the Company for any purpose, nor shall anything contained in this Warrant be construed to confer upon the Holder, solely in such Person’s capacity as the Holder, any of the rights of a shareholder of the Company or any right to vote, give or withhold consent to any corporate action (whether any reorganization, issue of stock, reclassification of stock, consolidation, merger, conveyance or otherwise), receive notice of meetings, receive dividends or subscription rights, or otherwise, prior to the issuance to the Holder of the Warrant Shares which such Person is then entitled to receive upon the due exercise of this Warrant. In addition, nothing contained in this Warrant shall be construed as imposing any liabilities on the Holder to purchase any securities (upon exercise of this Warrant or otherwise) or as a stockholder of the Company, whether such liabilities are asserted by the Company or by creditors of the Company. Notwithstanding this Section 6, the Company will provide the Holder with copies of the same notices and other information given to the stockholders of the Company generally, contemporaneously with the giving thereof to the stockholders.

7. REISSUANCE OF WARRANTS.

(a) Transfer of Warrant. If this Warrant is to be transferred, the Holder shall surrender this Warrant to the Company, whereupon the Company will forthwith issue and deliver upon the order of the Holder a new Warrant (in accordance with Section 7(d)), registered as the Holder may request, representing the right to purchase the number of Warrant Shares being transferred by the Holder and, if less then the total number of Warrant Shares then underlying this Warrant is being transferred, a new Warrant (in accordance with Section 7(d)) to the Holder representing the right to purchase the number of Warrant Shares not being transferred.

(b) Lost, Stolen or Mutilated Warrant. Upon receipt by the Company of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant, and, in the case of loss, theft or destruction, of any indemnification undertaking by the Holder to the Company in customary form and, in the case of mutilation, upon surrender and cancellation of this Warrant, the Company shall execute and deliver to the Holder a new Warrant (in accordance with Section 7(d)) representing the right to purchase the Warrant Shares then underlying this Warrant.

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(c) Warrant Exchangeable for Multiple Warrants. This Warrant is exchangeable, upon the surrender hereof by the Holder at the principal office of the Company, for a new Warrant or Warrants (in accordance with Section 7(d)) representing in the aggregate the right to purchase the number of Warrant Shares then underlying this Warrant, and each such new Warrant will represent the right to purchase such portion of such Warrant Shares as is designated by the Holder at the time of such surrender; provided, however, that no Warrants for fractional shares of Common Stock shall be given.

(d) Issuance of New Warrants. Whenever the Company is required to issue a new Warrant pursuant to the terms of this Warrant, such new Warrant (i) shall be of like tenor with this Warrant, (ii) shall represent, as indicated on the face of such new Warrant, the right to purchase the Warrant Shares then underlying this Warrant (or in the case of a new Warrant being issued pursuant to Section 7(a) or Section 7(c), the Warrant Shares designated by the Holder which, when added to the number of shares of Common Stock underlying the other new Warrants issued in connection with such issuance, does not exceed the number of Warrant Shares then underlying this Warrant), (iii) shall have an issuance date, as indicated on the face of such new Warrant, which is the same as the Issuance Date, and (iv) shall have the same rights and conditions as this Warrant.

8. NOTICES. Whenever notice is required to be given under this Warrant, unless otherwise provided herein, such notice shall be given in accordance with Section 9(f) of the Securities Purchase Agreement. The Company shall provide the Holder with prompt written notice of all actions taken pursuant to this Warrant, including in reasonable detail a description of such action and the reason therefore. Without limiting the generality of the foregoing, the Company will give written notice to the Holder (i) promptly upon any adjustment of the Exercise Price or number of Warrant Shares or number or kind of securities purchasable upon exercise of this Warrant, setting forth in reasonable detail, and certifying, the facts requiring such adjustment and the calculation of such adjustment and (ii) at least fifteen days prior to the date on which the Company closes its books or takes a record (A) with respect to any dividend or distribution upon the Common Stock, (B) with respect to any grants, issues or sales of any Options, Convertible Securities or rights to purchase stock, warrants, securities or other property to holders of Common Stock or (C) for determining rights to vote with respect to any Change of Control (as defined in the SPA Securities), dissolution or liquidation, provided in each case that such information shall be made known to the public prior to or in conjunction with such notice being provided to the Holder.

9. AMENDMENT AND WAIVER. Except as otherwise provided herein, the provisions of this Warrant may be amended and the Company may take any action herein prohibited, or omit to perform any act herein required to be performed by it, only if the Company has obtained the written consent of the holders of SPA Warrants representing at least a majority of the shares of Common Stock obtainable upon exercise of the SPA Warrants then outstanding; provided that no such action may increase the exercise price of any SPA Warrant or decrease the number of shares or class of stock obtainable upon exercise of any SPA Warrant without the written consent of the Holder. No such amendment shall be effective to the extent that it applies to less than all of the holders of the SPA Warrants then outstanding.

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10. GOVERNING LAW. This Warrant shall be construed and enforced in accordance with, and all questions concerning the construction, validity, interpretation and performance of this Warrant shall be governed by, the internal laws of the State of New York, without giving effect to any choice of law or conflict of law provision or rule (whether of the State of New York or any other jurisdictions) that would cause the application of the laws of any jurisdictions other than the State of New York.

11. CONSTRUCTION; HEADINGS. This Warrant shall be deemed to be jointly drafted by the Company and all the holders of SPA Warrants and shall not be construed against any person as the drafter hereof. The headings of this Warrant are for convenience of reference and shall not form part of, or affect the interpretation of, this Warrant.

12. DISPUTE RESOLUTION. In the case of a dispute as to the determination of the Exercise Price or the arithmetic calculation of the Warrant Shares, the Company shall submit the disputed determinations or arithmetic calculations via facsimile within two Business Days of receipt of the Exercise Notice giving rise to such dispute, as the case may be, to the Holder. If the Holder and the Company are unable to agree upon such determination or calculation of the Exercise Price or the Warrant Shares within three Business Days of such disputed determination or arithmetic calculation being submitted to the Holder, then the Company shall, within two Business Days submit via facsimile (a) the disputed determination of the Exercise Price to an independent, reputable investment bank selected by the Company and approved by the Holder or (b) the disputed arithmetic calculation of the Warrant Shares to the Company’s independent, outside accountant. The Company shall use reasonable best efforts to cause the investment bank or the accountant, as the case may be, to perform the determinations or calculations and notify the Company and the Holder of the results no later than ten Business Days from the time it receives the disputed determinations or calculations. Such investment bank’s or accountant’s determination or calculation, as the case may be, shall be binding upon all parties absent demonstrable error.

13. REMEDIES, OTHER OBLIGATIONS, BREACHES AND INJUNCTIVE RELIEF. The remedies provided in this Warrant shall be cumulative and in addition to all other remedies available under this Warrant and the other Transaction Documents (as defined in the Securities Purchase Agreement) at law or in equity (including a decree of specific performance and/or other injunctive relief), and nothing herein shall limit the right of the Holder right to pursue actual damages for any failure by the Company to comply with the terms of this Warrant. The Company acknowledges that a breach by it of its obligations hereunder will cause irreparable harm to the holder of this Warrant and that the remedy at law for any such breach may be inadequate. The Company therefore agrees that, in the event of any such breach or threatened breach, the Holder shall be entitled, in addition to all other available remedies, to an injunction restraining any breach, without the necessity of showing economic loss and without any bond or other security being required.

14. TRANSFER. This Warrant may be offered for sale, sold, transferred or assigned without the consent of the Company, except as may otherwise be required by Sections 2(f) and 2(g) of the Securities Purchase Agreement.

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15. CERTAIN DEFINITIONS. For purposes of this Warrant, the following terms shall have the following meanings:

(a) “Bloomberg” means Bloomberg Financial Markets.

(b) “Business Day” means any day other than Saturday, Sunday or other day on which commercial banks in The City of New York are authorized or required by law to remain closed.

(c) “Closing Bid Price” and “Closing Sale Price” means, for any security as of any date, the last closing bid price and last closing trade price, respectively, for such security on the Principal Market, as reported by Bloomberg, or, if the Principal Market begins to operate on an extended hours basis and does not designate the closing bid price or the closing trade price, as the case may be, then the last bid price or last trade price, respectively, of such security prior to 4:00:00 p.m., New York Time, as reported by Bloomberg, or, if the Principal Market is not the principal securities exchange or trading market for such security, the last closing bid price or last trade price, respectively, of such security on the principal securities exchange or trading market where such security is listed or traded as reported by Bloomberg, or if the foregoing do not apply, the last closing bid price or last trade price, respectively, of such security in the over-the-counter market on the electronic bulletin board for such security as reported by Bloomberg, or, if no closing bid price or last trade price, respectively, is reported for such security by Bloomberg, the average of the bid prices, or the ask prices, respectively, of any market makers for such security as reported in the “pink sheets” by Pink Sheets LLC (formerly the National Quotation Bureau, Inc.). If the Closing Bid Price or the Closing Sale Price cannot be calculated for a security on a particular date on any of the foregoing bases, the Closing Bid Price or the Closing Sale Price, as the case may be, of such security on such date shall be the fair market value as mutually determined by the Company and the Holder. If the Company and the Holder are unable to agree upon the fair market value of such security, then such dispute shall be resolved pursuant to Section 12. All such determinations to be appropriately adjusted for any stock dividend, stock split, stock combination or other similar transaction during the applicable calculation period.

(d) “Common Stock” means (i) the Company’s common stock, par value $0.01 per share, and (ii) any capital stock into which such Common Stock shall have been changed or any capital stock resulting from a reclassification of such Common Stock.

(e) “Common Stock Deemed Outstanding” means, at any given time, the number of shares of Common Stock actually outstanding at such time, plus the number of shares of Common Stock deemed to be outstanding pursuant to Sections 2(a)(i) and 2(a)(ii) hereof regardless of whether the Options or Convertible Securities are actually exercisable or convertible at such time, but excluding any shares of Common Stock owned or held by or for the account of the Company or issuable upon conversion of the SPA Securities or exercise of the SPA Warrants.

(f) “Convertible Securities” means any stock or securities (other than Options) directly or indirectly convertible into or exercisable or exchangeable for Common Stock.

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(g) “Expiration Date” means the date three years after the applicable Closing Date (as defined in the Securities Purchase Agreement) at which the Company’s obligation to issue this Warrant arose or, if such date falls on a day other than a Business Day or on which trading does not take place on the Principal Market (a “Holiday”), the next date that is not a Holiday.

(h) “Options” means any rights, warrants or options to subscribe for or purchase Common Stock or Convertible Securities.

(i) “Person” means an individual, a limited liability company, a partnership, a joint venture, a corporation, a trust, an unincorporated organization, any other entity and a government or any department or agency thereof.

(j) “Principal Market” means the Nasdaq National Market.

(k) “Registration Rights Agreement” means that certain registration rights agreement dated as of February 9, 2004, by and among the Company and the Buyers, as the same may be amended from time to time in accordance with the provisions thereof.

(l) “SPA Securities” means the senior convertible notes issued or issuable pursuant to the Securities Purchase Agreement.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company has caused this Warrant to Purchase Common Stock to be duly executed as of the Issuance Date set out above.

EXHIBIT A

EXERCISE NOTICE

TO BE EXECUTED BY THE REGISTERED HOLDER TO EXERCISE THIS

WARRANT TO PURCHASE COMMON STOCK

CORVIS CORPORATION

The undersigned holder hereby exercises the right to purchase              of the shares of Common Stock (“Warrant Shares”) of Corvis Corporation, a Delaware corporation (the “Company”), evidenced by the attached Warrant to Purchase Common Stock (the “Warrant”). Capitalized terms used herein and not otherwise defined shall have the respective meanings set forth in the Warrant.

1. Form of Exercise Price. The Holder intends that payment of the Exercise Price shall be made as:

             a “Cash Exercise” with respect to              Warrant Shares;

and/or

             a “Cashless Exercise” with respect to              Warrant Shares.

2. Payment of Exercise Price. In the event that the holder has elected a Cash Exercise with respect to some or all of the Warrant Shares to be issued pursuant hereto, the holder shall pay the Aggregate Exercise Price in the sum of $                     to the Company in accordance with the terms of the Warrant.

3. Delivery of Warrant Shares. The Company shall deliver to the holder              Warrant Shares in accordance with the terms of the Warrant.

Date:                          ,         

ACKNOWLEDGMENT

The Company hereby acknowledges this Exercise Notice and hereby directs Continental Stock Transfer & Trust Company to issue the above indicated number of shares of Common Stock in accordance with the Transfer Agent Instructions dated February         , 2004 from the Company and acknowledged and agreed to by Continental Stock Transfer & Trust Company.